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arXiv:0805.2120 · Europhysics Letters (EPL)

Quantum billiards in optical lattices

Simone Montangero, Diego Frustaglia, Tommaso Calarco, Rosario Fazio

Published Nov 1, 2009• 13 citations
arXivHTMLPDF

Abstract

We study finite two-dimensional spin lattices with definite geometry (spin billiards) demonstrating the display of collective integrable or chaotic dynamics depending on their shape.We show that such systems can be quantum simulated by ultra-cold atoms in optical lattices and discuss how to identify their dynamical features in a realistic experimental setup.Possible applications are the simulation of quantum information tasks in mesoscopic devices.

DOI
10.1209/0295-5075/88/30006

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We study finite two-dimensional spin lattices with definite geometry (spin billiards) demonstrating the display of collective integrable or chaotic dynamics depending on their shape.We show that such systems can be quantum simulated by ultra-cold atoms in optical lattices and discuss how to identify their dynamical features in a realistic experimental setup.Possible applications are the simulation of quantum information tasks in mesoscopic devices.
Summary form only given. One of the central paradigms for classical and quantum chaos in conservative systems is the two-dimensional billiard in which particles are confined to a dosed region in the plane, undergoing elastic collisions with the walls and free motion in between. We report the first realization of billiards using ultracold atoms bouncing off the beams of light. These beams create the desired spatial pattern, forming an "optical billiard". The system is extremely flexible due to the high level of control of the billiards geometry, the initial atomic sample, and the available measurement techniques. We find an excellent agreement between theory and our experimental demonstration of chaotic and stable motion in optical billiards, establishing a new experimental testing ground for classical and quantum chaos.
Summary form only given. The motion of a particle inside a closed area surrounded by reflecting walls can be integrable or chaotic, depending on the shape of the boundary. These billiards serve as a good and simple model to study chaotic dynamics both classically and quantum mechanically. Recently, we realized an "atom-optics billiard", where ultra-cold atoms are trapped inside a dark optical trap, whose shape can be varied to create different atom dynamics. In this work we describe how scattering and wall softness influence the dynamics of the atoms, and destroy or create stability.
We propose a method for optical visualization of the Bose-Hubbard model with two interacting bosons in the form of two-dimensional (2D) optical lattices consisting of optical waveguides, where the waveguides at the diagonal are characterized by different refractive indices than others elsewhere, modeling the boson-boson interaction. We study the light intensity distribution function averaged over the direction of propagation for both ordered and disordered cases, exploring the sensitivity of the averaged picture with respect to the beam injection position. For our finite systems, the resulting patterns are reminiscent the ones set in billiards, and therefore we introduce a definition of discrete quantum billiards and discuss the possible relevance to its well-established continuous counterpart.